Tuesday's jobs report should show that the employment picture improved slightly in September after a soft summer, but it will take several more months before markets trust the numbers to tell a clear story.

September's report, delayed by the government shutdown, will be released at 8:30 a.m. EDT Tuesday. It's expected to show 180,000 jobs were created and the unemployment rate unchanged at 7.3 percent, according to Reuters. There were 169,000 jobs added in August, but just 104,000 in July, after revisions.

The report, originally set for Oct. 4, had been anticipated as the most important piece of data the Fed would review before it meets next week, but it has become far less relevant because it is now stale and does not reflect the impact of the partial government shutdown. The 16-day closure also delayed the release of other data, including October's employment report, now expected Nov. 8 instead of Nov. 1.

"It's not going to be as much a driver of policy expectations as it might have been otherwise, so we wouldn't think it would have such a major impact on the Treasury market," said Ian Lyngen, senior Treasury strategist at CRT Capital. Lyngen said, however, if the number is a big surprise, the market will trade it. "But unlike prior employment reports, it doesn't feel like there's a great deal of positions put on ahead of it, and not a lot of risk being taken on either side."

The economic impact of the shutdown has yet to be seen, but it has made the view of the economy murkier because of the lack of all types of government data, now scheduled to be released gradually. The shutdown was resolved last week when Congress voted to push deadlines for a spending resolution to January and the debt ceiling to February.

"We think this will be a strong report. We're looking for 200,000 payrolls and a 0.1 drop in the unemployment rate," said Dean Maki,chief U.S. economist at Barclays. "Pretty much everything we look at suggested stronger payroll growth in September, than in the prior few months."

Maki said the September report should be the first in a string of better reports, reflecting a better environment for hiring. "We have not changed our call for a December tapering. If we're correct then jobs growth is strengthening notably over the next three months," Maki said.

Because of the government shutdown and uncertainty, the market has shifted its view for when the Fed might begin to "taper" or pare back its $85 billion in monthly bond buying. While December is still an option, some Fed watchers do not expect the Fed to slow its purchases until Fed chair nominee Janet Yellen's first meeting in March, or even later.

Some economists see a half percent hit on fourth quarter GDP growth from the shutdown, which should be somewhat made up in the first quarter of 2014.

(Read more: DC gets busy on to do list to avoid another crisis)

On Monday, one dovish Fed official weighed in on the lack of data and the question of tapering the Fed's purchases of Treasurys and mortgage-backed securities. Chicago Fed President Charles Evans told CNBC's Steve Liesman that it will be "tough" for the Fed to have sufficient confidence in the economic recovery by December.

When asked about the Fed tapering, he said the data pose problems. "October is a tough one. December? I think we need a couple of good labor reports and evidence of increasing growth, GDP growth. It's probably going to take a few months to sort that one out," Evans said on "Squawk Box."

J.P. Morgan economists expect the shutdown shaved 0.5 percent from GDP growth, and they now see a 2 percent fourth quarter growth rate. The economists expect 195,000 nonfarm payrolls were created in September, and that the shutdown should affect the next couple of employment reports.

"You're going to see some impact from the shutdown on the October employment report. It's going to be really hard to see how much that was and how much it matters. It does add uncertainty to the mix," said JPM economist Daniel Silver. He estimates that the October employment report will be reduced by 30,000 private and public sector jobs because of the shutdown.

"November's report is going to the be the reverse of the October report," he said, noting that the workers would return to work and inflate the October number.

Maki said he does not expect a major impact on employment data from the shutdown. He said he thinks most government workers remained on the payroll so the October report will be a better picture of reality than some expect. He also said the effect would then reverse in November.

Stephen Stanley, chief economist at Pierpont Securities, said there should not be much affect from government workers on the October report, but there could be an impact from the private sector. Stanley said the majority of government workers seem to be on a two-week pay period that ended Oct. 19 so they would have been counted as working during that period. He expects 165,000 payrolls for September.

"The problem is all the ripple effects, and those are not going to be readily identifiable in the data," he said. For instance, there could be a large number of restaurant workers out of work in October because they worked in or near national parks. Other small businesses could also have been hurt and temporarily laid off workers.

"I don't have a strong feeling of whether that's a big number or a small number," he said. By November, there should be a good indication of what the trend is. "At least then, you can do a two-month average - the November number should not be clean, but the two month average should be clean...all these people that would have temporarily laid off presumably should go back to work."